# Exam-Style Question on Statistics

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 715. This question is similar to one that appeared on a GCSE Higher paper in 2022. The use of a calculator is allowed.

(a) The list shows 18 temperatures, in degrees Celsius, at 2pm on different days in Honeyville.

 19 23 23 16 22 18 29 18 23 24 16 23 20 25 23 27 27 23

(i) Construct a stem-and-leaf diagram to show this information.

(ii) Find the median.

(iii) Find the lower quartile.

(iv) Graham draws a pie chart to show this information.

Calculate the sector angle for the number of days the temperature is 23°C.

(b) The box-and-whisker plot shows information about the masses, in grams, of some stones.

(i) Find the median.

(ii) Find the range.

(iii) Find the interquartile range.

(c) (i) The time, $$t$$ minutes, spent exercising in one week by each of 184 students is recorded. The table shows the results.

$$\begin{array}{|c|c|} \hline \text{Time } (t \text{ minutes}) & \text{Frequency} \\ \hline 40 < t \leq 60 & 5 \\ 60 < t \leq 80 & 12 \\ 80 < t \leq 90 & 55 \\ 90 < t \leq 100 & 90 \\ 100 < t \leq 150 & 22 \\ \hline \end{array}$$

Calculate an estimate of the mean.

(ii) A new table with different class intervals is completed.

$$\begin{array}{|c|c|} \hline \text{Time } (t \text{ minutes}) & \text{Frequency} \\ \hline 40 < t \leq 90 & 72 \\ 90 < t \leq 150 & 112 \\ \hline \end{array}$$

On a histogram the height of the bar for the $$40 < t \leq 90$$ interval is 7.2 cm.

Calculate the height of the bar for the $$90 < t \leq 150$$ interval.

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